© 2020, © 2020 The Author(s). Published by National Institute for Materials Science in partnership with Taylor & Francis Group. We propose a new theoretical kinetic model of strength recovery by oxidation-induced self-healing of surface cracks in composites containing a healing agent (HA). The kinetics is a key parameter in the design of structural components that can self-heal the damage done in service. Based on three-dimensional (3D) observations of crack-gap filling, two crack-gap filling models, i.e., a bridging model and a tip-to-mouth filling model, are incorporated in the proposed kinetic model. These crack-gap filling models account for the microstructural features of the fracture surfaces, crack geometry, and oxidation kinetics of the healing-agent. Hence, the minimum and maximum remaining flaw sizes in the healed crack gaps are estimated for various healing temperatures, times, and oxygen partial pressure conditions. Further, the nonlinear elastic fracture mechanics suitable for small-sized remaining flaws, together with a statistical analysis of the original Weibull-type strength distribution, enables the prediction of upper and lower strength limits of the healed composites. Three sintered alumina matrix composites containing silicon carbide (SiC)-type HAs with various volume fractions and shapes, together with monolithic SiC ceramics, are considered. The strength of the healed-composite predicted by our model agrees well with the experimental values. This theoretical approach can be applied to HAs other than SiC and enables the design of self-healing ceramic components for various applications.